A theoretical study of the modified equal scalar and vector Manning-Rosen potential within the deformed Klein-Gordon and Schrödinger in RNCQM and NRNCQM symmetries

Abstract

In this research work, within the framework of relativistic and nonrelativistic noncommutative quantum mechanics, the deformed Klein–Gordon and Schrödinger equations were solved with the modified equal vector scalar Manning-Rosen potential that has been of significance interest in recent years using Bopp's shift method and standard perturbation theory in the first-order in the noncommutativity parameters in 3-dimensions noncommutative quantum mechanics. By employing the improved approximation of the centrifugal term, the relativistic and nonrelativistic bound state energies were obtained for some diatomic molecules such as (HCl, CH, LiH, CO, NO, O2, I2, N2, H2, and Ar2). The obtained energy eigenvalues appear as a function of the generalized Gamma function, the parameters of noncommutativity, and the parameters of studied potential, in addition to the atomic quantum numbers . In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present result is consistent with what is obtained in the literature. We have seen that the improved approximation of the centrifugal term is better than the other approximations in finding the approximate analytical solutions of the Klein-Gordon and Schrödinger equations for the modified Manning–Rosen potential in RNCQM and NRNCQM.

The Impact of deformed space-phase parameters into HAs and HLM systems with the improved Hulthen plus Hellmann potentials model in the presence of temperature-dependent confined Coulomb potential within the framework of DSE

“…To perform this task the physical form of the deformed Schrödinger equation DSE, it is necessary to replace the ordinary threedimensional Hamiltonian operators H hhp (p, x), ordinary energy E hhp nl and corresponding complex wave function Ψ ( − → r ) in the symmetries of NRQM by three-dimensional Hamiltonian operators H hhp nc (p nc , x nc ), new unknown values E hhp nc of energy and corresponding new complex wave function Ψ ( − → r nc ), respectively, in 3DNRQM-NCSP symmetries. In addition, we need to replace the ordinary product with the star product ( * ), this allows us to construct the DSE in (NC-3D: RSP) symmetries as (see, e.g., [52][53][54][55][56]):…”

Analytical Expressions to Energy Eigenvalues of the Hydrogenic Atoms and the Heavy Light Mesons in the Framework of 3D-NCPS Symmetries Using the Generalized Bopp's Shift Method

“…The new coupling Lη is L x η 12 + L y η 23 + L z η 13 while LΘ is defined in the first section. It should be noted that GBSM has been successfully applied at the relativistic level in the field of high energies using both the Klein-Gordon equation [65][66][67][68][69][70][71][72][73][74][75][76][77][78], Dirac equation [79][80][81] and Duffin-Kemmer-Petiau equation [82]. Thus, the reduced SE (without star product) can be written as…”

The Effects of Noncommutativity on the Energy Spectra for Mass-Dependent Klein-Gordon and Shrödinger Equations with Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential: Application to HLM Systems

“…To overcome these numerous challenges, physicists considered expanding the known symmetries of quantum mechanics, which are based on x (S,H,I) ncµ , p (S,H,I) ncν = 0, to include new postulates (see Refs. [20][21][22][23][24][25][26][27][28][29]):…”